Transcript Document 7139675

The Evolving Block Universe:
A more realistic view of spacetime
geometry
George Ellis
University of Cape Town
AIMS
December 2012
“Space time and the passage of
time”: G Ellis, arXiv:1208.2611
1: A standard physics picture:
Time is an illusion
 The Block Universe
2: Taking time seriously:
Time passes, as regards:
- The contents of spacetime
- Spacetime itself
The Emergent Block Universe
 but there are objections …….
3: Taking quantum theory seriously:
- Collapse of the wave function as the transition
event
- Delayed choice
 The Crystallizing Block Universe
1: Time as an Illusion
The nature of spacetime in both special and general relativity
has lead some to a view that the passage of time is an illusion.
Given data at an arbitrary time, it is claimed that everything
occurring at any later or earlier time can be uniquely
determined from that data. Time reversible Hamiltonian
dynamics provides the basis for physics in general, and
gravitation in particular. One can predict equally to the past
and the future from present day data.
H: S(x0,t0)  S(x1,t1) for all t0, t1
Consequently, nothing can be special about any particular
moment; there is no special “now” which can be called the
present.
Past, present and future are equal to each other, for there is no
“In The End of
Time, which is
written both for the
popular-science
market and for
scientists and
philosophers, I
argue that the
apparent passage of
time is an illusion. If
we could stand
outside the universe
and ‘see it as it is’, it
would appear to be
static.”
The Block Universe
Such a view can be formalized in the idea of a Block
Universe: space and time are represented as merged into
an unchanging spacetime entity, with no particular
space sections identified as the present and no evolution
of spacetime taking place.
The universe just is: a fixed spacetime block,
representing all events that have happened and that will
happen.
This representation implicitly embodies the idea that
time is an illusion: time does not “roll on” in this
picture.
All past and future times are equally present, and the
present “now” is just one of an infinite number.
The block universe: Both the past and the future already
exist, and are uniquely determined. Nothing unexpected can
happen. The present has no significance.
The problem with this view is that it is profound contradiction
with our experiences in everyday life, and in particular with
the way science is carried out. Scientific theories are developed
and then tested by an ongoing process that rolls out in time:
initially the theory does not exist; it is developed, tested,
refined, finally perhaps accepted: as in other cases, events
take place!
By contrast to this view, one can suggest that the true nature of
spacetime is best represented as an Emergent Block Universe
(EBU), a spacetime which grows and incorporates ever more
events, “concretizing” as time evolves along each world line.
Unlike the standard block universe, it adequately represents
the differences between the past, present, and future, and
depicts the change from the potentialities of the future to the
determinate nature of the past.
2: Taking time seriously:
Things actually happen in time!
The macro – micro tension:
Reversible laws at micro level:
Hamiltonian dynamics
Irreversible at macro level:
Second law of thermodynamics.
- The fundamental feature of the macro world of
physics chemistry and biology
- e.g. breaking a glass (Penrose); process of life
In the real world: The past and future are not
predictable from the present: not Hamiltonian!
The solar system undergoes time-reversible
Hamiltonian allowing exquisite prediction.
BUT This is the exception rather than the rule;
It allows very accurate prediction to the future and
the past in this specific (almost frictionless) case: for
a limited time. This is highly exceptional.
Arthur Stanley Eddington (1882-1944))
The Second Law of Thermodynamics:
Entropy (randomness) always increases
“If someone points out to you that your pet theory of the
universe is in disagreement with Maxwell's equations —
then so much the worse for Maxwell's equations.
If it is found to be contradicted by observation — well, these
experimentalists do bungle things sometimes.
But if your theory is found to be against the second law of
thermodynamics I can give you no hope; there is nothing
for it but to collapse in deepest humiliation.”
Classical physics in the real world is not
Hamiltonian!
(at macro scales): dissipation takes place,
dS/dt >0
Is it reversible at the micro scale but not at the
macro scale? The apparent flow of time is just
a result of coarse graining – and hence an
illusion?
No: complex systems really undergo time
change! (at the macro scale)
What about micro scales? Collapse of the
wave function takes place: also time
Taking time seriously:
An evolving block spacetime
Consider a massive object with two computer
controlled rocket engines that move it right or left
Let the computer determine the outcome on the
basis of measurements of decay products of excited
atoms
Then the outcome is unpredictable in principle
If the object is massive enough: it curves spacetime
The future spacetime structure is not determinable
The change from uncertainty to certainty:
the present is where the indefinite future changes to the
determined past
Bohr–Einstein debates [wikipedia]
Bohr response :since the system is immersed in a gravitational potential
which varies with the position, according to the principle of equivalence the
uncertainty in the position of the clock implies an uncertainty with respect to
its measurement of time and therefore of the value of the interval. A precise
evaluation of this effect leads to the conclusion that the relation cannot be
violated.
The evolving block universe grows with time:
• The past has been determined and is fixed,
• The future is uncertain and still has to be fixed
Because of quantum uncertainty, it is not true that
the future is determined at the present
• The present is where the change takes place.
It is crucially different from the past and future,
and indeed separates them.
The future does not exist in the same sense as the past
or the present.
The determinate region grows with time.
Spacetime itself is growing.
The evolving block universe (EBU):
Spacetime grows with time
The evolving block universe (EBU):
Spacetime grows with time
The evolving block universe (EBU):
Spacetime grows with time
The evolving block universe (EBU):
Spacetime grows with time
The paradox
This model of spacetime is obviously far more in
accord with our daily experience than the standard
Block Universe picture; indeed everyday data,
including the apparent passage of time involved in
carrying out every single physics experiment, would
seem to decisively choose the EBU over the Block
Universe.
The evidence seems abundantly clear. Why then do
some physicists prefer the latter?
If the scientific method is to abandon a theory when the
evidence is against it, why do some hold to it?
This counter viewpoint is put succinctly by Sean Caroll in a
blog:
“The past and future are equally real. This isn’t completely
accepted, but it should be. Intuitively we think that the ‘now’
is real, while the past is fixed and in the books, and the future
hasn’t yet occurred. But physics teaches us something
remarkable: every event in the past and future is implicit in
the current moment. This is hard to see in our everyday lives,
since we’re nowhere close to knowing everything about the
universe at any moment, nor will we ever be - but the
equations don’t lie. As Einstein put it, ‘It appears therefore
more natural to think of physical reality as a four dimensional
existence, instead of, as hitherto, the evolution of a three
dimensional existence.’ ”
But the question is which equations, and when are they
applicable?
When true complexity is taken into account, the unitary
equations leading to the view that time is an illusion are
generically not applicable except to isolated micro components
of the whole.
The viewpoint expressed by Carroll supposes a determinism of
the future that is not realised in practice: inter alia, he is
denying the existence of quantum uncertainty in the universe
we experience.
But physics experiments show that uncertainty to be a well
established aspect of the universe, and it can have macroscopic
consequences in the real world, as is demonstrated by the
historic process of structure formation resulting from quantum
fluctuations during the inflationary era. These inhomogeneities
Expansion history
Quantum fluctuations
Unpredictable galaxies
time
• The prime issue arising is that the spacetime view of special
relativity denies the existence of any preferred time slices,
whereas the claimed existence of the present in the EBU is
certainly a preferred time surface (at each instant, it is the
future boundary of the 4-dimensional spacetime). I consider
this first.
• An array of further arguments for the claim “time is an
illusion” have been made by philosophers and physicists are
summarized in the Spring, 2012 special issue of Scientific
American. I will turn to them next.
• I then consider the way the Block Universe view relates to
theories of the mind: a key problem for that view.
• I point out how it relates to the arrow of time issue and solves
the chronology protection issue
• Finally I consider how the EBU picture may be altered when
one takes quantum issues into account
3: Surfaces of change
The primary problem is the claimed unique status of “the
present” in the EBU - the surface where the indeterminate
future is changed to the definite past at any instant.
It is a fundamental feature of Special Relativity that
simultaneity is not uniquely defined, it depends on the state
of motion of the observer. What is past and future elsewhere
depends on one’s motion,
For different observers at a event P, different motions will
designate different events Q on a distant world line L as
simultaneous with P.
Hence the block universe model is natural: it is the only way
a spacetime model can incorporate this lack of well defined
surfaces of instantaneity. Hence time is an illusion
The block universe: time sections move on ….
But they are they are arbitrary – depending on the observer’s
motion
Einstein: SR they are arbitrary – depending on the
observer’s motion
Resolution:
Physically, things happen along timelike worldlines rather
than on spacelike surfaces
Time of determination: Start at the beginning of time,
measure proper time along fundamental world lines: thereby
determine the transition surfaces (“the present”) as time
evolves along preferred fundamental world lines.
This is not globally coordinated by some non-local
mechanism: rather it happens locally everywhere
So change happens on preferred surfaces of change that are
secondary to timelike world lines.
These surfaces need not be simultaneous in the usual sense
Simultaneity as usually defined, determined by radar, is irrelevant
to physical causation!
Physically, things happen along timelike worldlines
rather than on spacelike surfaces
E3
S?
E2
E1
What matters physically is E1 (emission), E2 (interaction),
and E3 (reception);
Which event S is simultaneous with E2 has no physical
significance: it only has psychological value.
What really matters is proper time measured along timelines
xi(v), determined by the metric tensor gij (xk) by the basic
formula
τ = ∫ (−ds2)1/2 = ∫ (-gij(dxi/dv)(dxj/dv))1/2 dv (*)
Natural surfaces of constant time are given by this integral
since the start of the universe. Thus we can propose that
The present: The ever-changing surface S(τ) separating the
future and past - the ‘present’ - at the time τ is the surface {τ =
constant} given by integral (*) along a family of fundamental
world lines starting at the beginning of space time.
(if the universe existed forever we have to start at some
arbitrarily chosen ‘present’ time {τ0 = const}, which we
assume exists, and integrate from there).
But is this well defined, given that there are no preferred
world-lines in the flat spacetime of special relativity?
The second fundamental feature is that it is general relativity
that describes the structure of space time, not special
relativity. Gravity governs space-time curvature,
Because there is no perfect vacuum anywhere in the real
universe (inter alia because cosmic blackbody background
radiation permeates the Solar System and all of interstellar
and intergalactic space), space time is nowhere flat or even of
constant curvature;
Therefore there are preferred timelike lines everywhere in any
realistic spacetime model.
The special relativity argument does not apply.
A unique geometrically determined choice for fundamental
worldlines is the set of timelike eigenlines xa(v) of the Ricci
tensor on a suitable averaging scale (they will exist and be
unique for all realistic matter, because of the energy
conditions such matter obeys).
Their 4 velocities ua (v) = dxa(v)/dv satisfy
Tab ub = λ1 ua ⇔ Rab ub = λ2 ua (**)
where the equivalence follows from the Einstein field
equations.
Thus we can further propose that
Fundamental world lines: the proper time integral (*) used
to define the present is taken along the world lines with 4velocity ua(v) satisfying (**).
This will give the usual surfaces of constant time in the
The evolving block universe:
the present is where the future changes to the past
Takes place along preferred timelike worldlines:
The average motion of matter in the universe
• What about simultaneity?
In general these surfaces are not related to simultaneity as
determined by radar; indeed this is even so in the FLRW
spacetimes (where the surfaces of homogeneity are generically
not simultaneous, according to the radar definition).
The flow lines are not necessarily orthogonal to the surfaces of
constant time;
More than that: the surfaces determined in this way are not
even necessarily spacelike, in an inhomogeneous spacetime.
These surfaces are secondary to the timelike world lines that
define them. No physical phenomena are directly determined
by simultaneity in the usual sense.
• 4 An array of further arguments
• Further arguments for the claim “time is an illusion” have
been made by philosophers and physicists are summarized
in the January, 2012 special issue of Scientific American; also
Tim Maudlin, The Metaphysics within Physics.
•
•
•
•
•
•
A: Rates of change?
B: Time parameter invariance?
C: General covariance and local Lorentz invariance?
D:The Wheeler de Witt Equation and lack of cosmic time
[E: Categorization problem]
[F: Not necessary to describe events]
I consider them in turn. For detailed response, see
arXiv:1208.2611
Scientific American,
Special issue,
January 25, 2012:
“A Matter of Time”
This special issue of
Scientific American
summarizes what
science has discovered
about how time
permeates and guides
both our physical
world and our inner
selves
A: Rates of change
A key question is, “How fast does time pass?” Davies, Carr,
and others suggest there is no sensible answer to this
question.
I claim that the answer is given by the metric tensor gij(xk),
which determines proper time τ along any world line:
τ = ∫ (−ds2)1/2 = ∫ (-gij(dxi/dv)(dxj/dv))1/2 dv (*)
This is the time measured along that world line by any
perfect clock; time changes at the rate of 1 second per second
[Maudlin]. This is what fixes physical time, including
gravitational time dilation [gravitational potential affects
relative rates].
Real world clocks - oscillators that obey the Simple
Harmonic Equation - are approximations to such ideal
The metric evolution: So if the metric tensor determines
proper time, what determines the metric tensor?
The Einstein field equations, of course! Following ADM, the
first fundamental form (the metric) is represented as
ds2 = (−N2 + NiNi)dt2 + Nidxjdt + gijdxidxj
where i, j = 1, 2, 3. The lapse function N(x) and shift vector
Ni(x) represent coordinate choices, and can be chosen
arbitrarily; gij(x) is the metric of the 3-spaces {t = const}.
The second fundamental form is
πij = ni;j
where the normal to the surfaces {t = const} is ni = δ0i;
the matter flow lines have tangent vector ui = δi0
(which differs from ni = gijnj whenever Ni ≠ 0)
ADM coordinates:
Ni
Matter flow
Lapse
Shift Vector Ni(xj) gives the change of the matter lines
relative to the normal to the chosen time surfaces
Lapse function N(xi) gives the relation between coordinate
time and proper time along the normal lines
The field equations for gij(xk) are as follows (where
3-dimensional quantities have the prefix (3)): four constraint
equations
+ π2 − πijπij = 16π ρH, (C1)
Rμ := −2 πμj|j = 16π Tμ0
(C2)
(3)R
where “|j′′ represents the covariant derivative in the 3-surfaces, and
twelve evolution equations
∂t gij = 2Ng−1/2(πij −1/2gijπ) + Ni|j + Nj|i,
(T1)
∂tπij = −Ng−1/2((3)Rij −1/2gij(3)R) +1/2Ng−1/2gij(πmnπmn −1/2π2)
− 2Ng−1/2(πimπmj−1/2ππij) + √g(N|ij − gijN|m|m) + (πijNm)|m
− Ni|mπmj − Nj|mπmi + 16π (3)Tij.
(T2)
What determines how the matter evolves?
Equations of state for matter terms in (C1), (C2), (T2) must be
ab
This can be worked out using any time surfaces (that is the
merit of the ADM formalism); in particular one can choose a
unique gauge by specialising the time surfaces and flow lines
to those defined above
1. We choose the flow lines to be Ricci Eigenlines:
Tμ0 = 0 ⇒ Rμ = − 2 πμj|j =0
(G1)
which algebraically determines the shift vector Ni(xj),
thereby solving the constraint equations (C1);
2. We determine the lapse function N(xi) by the condition
that the time parameter t measures proper time τ along the
fundamental flow lines:
ds2 = - dτ2 
N2 = 1 + NiNi
(G2)
These conditions uniquely determine the lapse and shift.
Then,
• given the equations of state and dynamical equations for
the matter, equations (T1), (T2) determine the time evolution
of the metric in terms of proper time along the fundamental
flow lines;
• the constraints (C1), (C2) are conserved because of energymomentum conservation.
The development of spacetime with time takes place just as is
the case for other physical fields, with the relevant time
parameter being proper time τ along the fundamental flow
lines.
There is no problem with either the existence or the rate of
flow of time. Time flows at rate of one second per second, as
determined by the metric tensor locally at each event.
Predictability: Do these equations mean the spacetime
development is uniquely determined to the future and the
past from initial data? That all depends on the equations
of state of the matter content: one can have an explicitly
time dependent equation of state:
p =1/3gij (3)Tij, Πij = (3)Tij − p gij = F(τ) Πij(0)
where F(τ) represents local dynamics involving random
processes generated via quantum uncertainty.
So equations (T1), (T2) determine the time evolution of the
spacetime, but do not guarantee predictability.
If quantum unpredictability gets amplified to macro
scales, the spacetime evolution is intrinsically
undetermined till it happens (as during the generation of
seed inhomogeneities in the inflationary era in the very
B: Time parameter invariance
What about the time parameter invariance of General
Relativity, as made manifest in the ADM formalism?
• The gravitational side of the ADM equations may be timeparameter invariant, but the matter side is not;
• In particular when L = T – V = ½ m u2 –V(r), rescaling time
changes the kinetic energy T(u) while leaving the potential
energy V(r) unchanged: will give different orbits.
• Change t  t’ = f(t) leaves L invariant iff u’2 = u2  f(t) = t +
c.
Hence any solutions with matter present (i.e. all realistic
solutions) will not be time parameter invariant (changing t
f(t), there are similar solutions; but they are not the same)
This is part of the ongoing tension between the geometric and
Local physics does indeed have a preferred time
parameter: e.g. for a Simple Harmonic Oscillator using
standard time t, q(τ) = Acos(ωt); these cycles measure
physical time t like a metronome (which is why SHO’s are
used as clocks).
It applies equally to all local physics: each involves time t:
- Newton’s laws of motion
- Maxwell’s equations
- Schroedinger equation
- Dirac equation
- Diffusion equation
It is perverse to use any other time parameter for local
physics
This parameter t is just proper time τ measured along
relevant world lines, which provides a preferred time
C: General covariance and Lorentz
invariance?
What about general covariance and local Lorentz invariance?
These are symmetries of the general theory, not of its
solutions. Interesting solutions break the symmetries of the
theory: this is
not surprising, as we know that broken symmetries are the
key to interesting physics.
• Specific solutions of the theory have less symmetry than the
theory itself; this symmetry breaking is a key feature of all
realistic solutions of the equations of physics, and in particular
cosmological solutions
D: The Wheeler de Witt equation and
the mind
Julian Barbour: The End of Time
There is no time: the entire universe and everything in it
is static and unchanging.
Why? The Wheeler-de Witt equation
∂Ψ/ ∂t = H Ψ;
General relativity
H Ψ = 0  ∂Ψ/ ∂t = 0
Time is an illusion!
So how do we get the illusion of change?
Barbour claims there exist records of events that our brains read
sequentially, and so create a false illusion of the passage of time.
Thus brain processes are responsible for illusion of change.
The prevalent view of present day neuroscience is that mental
states Φ are functions of brain states B which are based in the
underlying neuronal states bi, determined by genetics and
interactions in the brain, taking place in the overall environment
E.
Φ = Φ(B) = Φ(bi, E).
If time does not flow in microphysics, in an unchanging
environment
{dbi/dt = 0, dE/dt = 0} ⇒ dΦ/dt = 0:
Mental states cannot evolve! [Maudlin]
We do know is that time does flow in our experience. Hence
the assumption that time does not flow in the underlying
physics cannot be true: the data proves it to be wrong.
The implication runs the other way: Taking everyday life
seriously, and comparing the claim ‘time is an illusion’ with
the evidence from mental life, the contradiction between them
is proof the WdeW equation does not apply to the universe as
a whole at the present time, as proposed by Barbour.
The great merit of Barbour’s book is that it takes the Wheeler
de Witt equation seriously, and pursues the implications to
their logical conclusion; the evidence from daily life then
shows it to be wrong
This argument applies equally to all claims that time is an
illusion
- The experience of the flow of time is based in brain physics
Arnowitt, Deser and Misner write of the Hamiltonian
formalism as follows:
“Since the relation between qM+1 and τ is undetermined, we
are free to specify it explicitly, i.e., impose a “coordinate
condition”. If, in particular, this relation is chosen to be qM+1
= τ (a condition which also determines N), the action (2.4)
then reduces [to] (2.5) with the notational change qM+1 → τ ;
the non-vanishing Hamiltonian [only] arises as a result of
this process.”
• This is the choice made above;
• the corresponding Hamiltonian will be non-zero as
indicated in this quote,
• so WdeW will not hold: ∂Ψ/ ∂t ≠ 0.
[as is also the case for unimodular gravity].
Critique of the Wheeler-DeWitt equation
Asher Peres
The Wheeler-DeWitt equation is based on the use of
canonical quantization rules that may be inconsistent for
constrained dynamical systems, such as minisuperspaces
subject to Einstein's equations. The resulting quantum
dynamics has no classical limit and it suffers from the
infamous ``problem of time.''
In this article, it is shown how a dynamical time (an internal
clock) can be constructed by means of a Hamilton-Jacobi
formalism, and then used for a consistent canonical
quantization, with the correct classical
arXiv:gr-qc/9704061
More fundamentally:
• Quantum mechanics applied to the real universe does NOT
only involve unitary transformations.
Measurements happen; collapse of the wave function takes
place; classical outcomes occur
-- NOT just decoherence: non unitary transformations take
place.
Ignoring this is ignoring a fundamental feature of physics.
So claiming there is only unitary WdeW evolution is simply not
correct: it is taking into account only part of the dynamics
occurring [Penrose]. Wave function collapse allows time to pass.
5: The arrow of time and
chronology protection
How can a difference emerge between the future and the
past, on the basis of time symmetric micro physics?
How does time know which way to flow?
Why does it flow the same way everywhere?
There is no basis for such a determination in
microphysics alone: the H-theorem (Boltzmann or QFT)
applies equally in both time directions.
It cannot provide a foundation for the second law of
thermodynamics with a unique arrow of time.
Micro physics(except weak interactions) is time symmetric. The
future and past are equal. How does macro physics know the
direction of time? In the block universe: they are equal.
Not so according to the second law of thermodynamics!
The direction of time:
In an EBU, the arrow of time arises fundamentally because
the future does not yet exist: a global asymmetry in the
physics context.
The Feynman propagator can only be integrated over the
past, as the future spacetime domain is yet to be determined.
One can be influenced at the present time from many causes
lying in our past, as they have already taken place and their
influence can thereafter be felt.
One cannot be physically influenced by causes coming from
the future, for they have not yet come into being.
This is the rationale for saying the past exists but the future
does not: if something can influence you, it exists.
The evolving block universe: the past exists and is
developing to the future, which does not yet exist.
It is this asymmetry that leads to the arrow of time.
Special initial conditions then lead to the 2nd law.
Future can’t affect today:
-Not yet definite what it is
-Possibilities exist, not outcomes
Past affects today:
-Elements
-Particles
-Radiation
Hence it must exist, else effect with no cause
Note 1: What happens earlier is mediated by what happens
later, i.e. its effects pass through the intervening times; still the
essential cause lies at earlier times
e.g. the fact that C, N, O exist in this room is due to
nucleosynthesis a time T* ago in the past, inside a star that lies
inside our physical horizon [Ellis and Stoeger:
arXiv:1001.4572];
-- These elements were preserved and passed on through
subsequent times (conservation laws!) but the causeof their
existence is at the earlier time T* < t0
Note 2: It is NOT due to subsequent existence of these elements
at later times t’ > t0 (the causal mechanism lies at earlier
times!)
Note 3: This story has decoupled the passage of time from the
growth of entropy. Given the passage of time, entropy will
Chronology protection
A longstanding problem is that closed timelike lines can occur
in exact solutions of the Einstein Field Equations with
reasonable matter content. This opens up the possibility of
many paradoxes, such as killing your own grandparents
before you were born and so creating causally untenable
situations.
It has been hypothesized that a Chronology Protection
Condition would prevent this happening. This is an add on to
the EFE: a selection condition for acceptable solutions.
Various arguments have been given in its support, but this
remains an ad hoc condition added on as an extra
requirement on solutions of the Einstein field equations,
Chronology protection
The EBU automatically provides such protection, because
creating closed timelike lines requires the undetermined
part of spacetime intruding on regions that have already
been fixed.
This would require the fundamental world lines to
intersect;
But if the fundamental world lines intersect, density
diverges,
a spacetime singularity occurs, the worldlines are
incomplete in the future, and time comes to an end there;
so no “Grandfather Paradox” can occur.
Hence the EBU as outlined above automatically provides
6 Taking quantum theory
seriously:
A: Unitary Evolution is not all that happens:
Real QM is non-unitary and irreversible when wave
function projection takes place
This is the core of the flow of time
B: Reaching back into the past
There are many hints that the future can influence the
past in quantum theory
• Wheeler: Delayed choice experiments
• Aharanov et al: Two-time formalism
Can represent by a Crystalising Block Universe
C: EPR and causality
This resolves the causal puzzle of apparently instantaneous
6 Taking quantum theory
seriously:
Unitary Evolution is not all that happens:
Real QM is non-unitary and irreversible when wave
function projection takes place
This is the core of the flow of time:
The indefinite future becomes the definite past as wave
function collapse takes place
This happens all the time everywhere
It does not need to relate to an experiment.
A: Quantum physics and Measurement
Schroedinger evolution is unitary and time reversible:
Ψ2 = U21 Ψ1
But this Is not all that happens!
Collapse of the wave function is where the indeterminateness
of the future gives way to the definite state of the past. Things
happen in quantum physics!
The outcome is unpredictable from past data: and this is
where real dynamic change takes place.
Quantum physics is not time reversible!
Claims that it is (e.g. referring only to Hamiltonian dynamics)
ignore measurements – a crucial feature of the theory
If a measurement of an observable A takes place at time t = t*,
initially the wave function ψ(x) is a linear combination of
eigenfunctions un(x) of the operator à that represents A:
for t < t*, the wave function is
ψ1(x) = Σn ψn un(x).
(1)
But immediately after the measurement has taken place,
the wave function is an eigenfunction of Ã:
ψ2(x) = aN uN(x)
(2)
for some specific value N. The data for t < t* do not determine the
index N; they just determine a probability for the choice N. One
can think of this as due to the probabilistic time-irreversible
collapse of the wave function.
The initial state (1) does not uniquely determine the
final state (2); and this is not due to lack of data, it is
due to the foundational nature of quantum
interactions.
You can predict the statistics of what is likely to
happen but not the unique actual physical outcome,
which unfolds in an unpredictable way as time
progresses; you can only find out what this outcome is
after it has happened.
Hypothesis: This is where the flow of time takes place: the
uncertainty of the future changes to the certainty of the
past. This happens all the time everywhere.
[G Ellis: arxiv:1108.5261]
Furthermore, in general the time t* is also not
predictable from the initial data: you don’t know when
`collapse of the wave function’ (the transition from (1)
to (2)) will happen (you can’t predict when a specific
excited atom will emit a photon, or a radioactive
particle will decay).
We also can’t retrodict to the past at the quantum level,
because once the wave function has collapsed to an
eigenstate we can’t tell from its final state what it was
before the measurement,
Knowledge of these later states does not suffice to
determine the initial state (1) at times t < t*:
The set of quantities ψn are not determined by the
single number aN.
How does this relate to the earlier part:
The EBU idea?
Why should the collapse of the wavefunction relate to
the average motion of matter in the universe?
-Because it is a contextually dependent effect:
-determined by the local physical environment, such
as the measurement apparatus, or any physical
system that causes collapse of the wave function
(screen, leaf, etc)
-See arxiv/1108.5261 for in depth discussion
When does collapse take place?
- an unanswered question.
Schrödinger’s cat!
B: Reaching Back into the Past
There are many hints that the future can influence the
past in quantum theory
• Wheeler and Feynman
- Advanced and retarded potentials
• Aharanov and collaborators
- Two-time formalism, weak measurement
•Cramer: Transactional quantum mechanics
•Wheeler: Delayed choice experiments
The Crystaliziing Block universe
Rothman and Ellis: arXiv0912.0808
The delayed choice experiment: affecting the quantum past
Wheeler's delayed choice experiment is a thought experiment
proposed by John Archibald Wheeler in 1978. Wheeler
proposed a variation of the famous double-slit experiment of
quantum physics, one in which the method of detection can
be changed after the photon passes the double slit, so as to
delay the choice of whether to detect the path of the particle,
or detect its interference with itself.
Since the measurement itself seems to determine how the
particle passes through the double slits, and thus its state as a
wave or particle, Wheeler's thought experiment seems to
demonstrate an ability to influence the past.
An implementation of the experiment in 2007 showed that
the act of observation ultimately decides whether the photon
will behave as a particle or wave, verifying the unintuitive
results of the thought experiment
Experimental realization of Wheeler's delayed-choice
GedankenExperiment
Vincent Jacques, E. Wu, Frédéric Grosshans, François
Treussart, Philippe Grangier, Alain Aspect, Jean-François
Roch
Science 315, 5814 (2007) 966 [arXiv:quant-ph/0610241v1]
Abstract: The quantum "mystery which cannot go away" (in
Feynman's words) of wave-particle duality is illustrated in a
striking way by Wheeler's delayed-choice Gedanken
Experiment.
In this experiment, the configuration of a two-path
interferometer is chosen after a single-photon pulse has
entered it : either the interferometer is closed i.e. the two paths
are recombined) and the interference is observed, or the
interferometer remains open and the path followed by the
Experimental realization of Wheeler's delayed-choice
GedankenExperiment
Vincent Jacques, E. Wu, Frédéric Grosshans, François Treussart,
Philippe Grangier, Alain Aspect, Jean-François Roch
“We report an almost ideal realization of that Gedanken
Experiment, where the light pulses are true single photons,
allowing unambiguous which-way measurements, and the
interferometer, which has two spatially separated paths,
produces high visibility interference.
The choice between measuring either the 'open' or 'closed'
configuration is made by a quantum random number generator,
and is space-like separated -- in the relativistic sense -- from the
entering of the photon into the interferometer. Measurements in
the closed configuration show interference with a visibility of
94%, while measurements in the open configuration allow us to
determine the followed path with an error probability lower than
1%. “
"A Delayed Choice Quantum Eraser"
by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlon O. Scully
http://xxx.lanl.gov/pdf/quant-ph/9903047
Phys.Rev.Lett. 84 1-5 (2000).
Abstract: This paper reports a "delayed choice quantum eraser"
experiment proposed by Scully and Drühl in 1982. The experimental
results demonstrated the possibility of simultaneously observing both
particle-like and wave-like behavior of a quantum via quantum
entanglement.
The which-path or both-path information of a quantum can be erased or
marked by its entangled twin even after the registration of the quantum.
How can we accommodate this in our spacetime picture?
The part of spacetime where quantum determination of a
definite state occurs is almost the same as the classical (Coarse
grained) present: but small bits lag behind and crystallize out
later.
Those ever decreasing domains are the space-time events
where we can influence “the past” from the present.
Gradually the crystalised out state comes to encompass the
whole of the matter present now. But at any time there will be
other unsettled regions that will be determined in the future.
This picture is already confirmed by experiment: it is what is
needed in order to make sense of the delayed choice
experiments.
May take place in two stages: 1st decoherence (decay of
entanglement), and then collapse of the wave function.
The crystallizing block universe:
the surface where the quantum uncertainty changes
to the classical definiteness
The crystalising block universe (EBU):
Spacetime grows with time: some places lag
The crystalising block universe (EBU):
Spacetime grows with time: some places lag
The crystalising block universe (EBU):
Spacetime grows with time: some places lag
Also some may lead!
C: EPR and Causality
Resolves the issue of instantaneous action in the
EPR experiment
- Determination of spin of one of a pair of
entangled particles instaneouslsy determines spin
of the other
Problematic because
A: Instantaneous action at a distance
B: Instantaneity ambiguous: depends on motion
Resolution: effect reaches back in to the past and
determines both spins at the emission event
The usual EPR interpretation: spooky action at a
distance. Note that if Alice or Bob move relative
to the source, then simultaneity will be
ambiguous according to who defines it.
LA
LS
E1
LB
E2
E0
The revised proposal: reaching back into the past.
Note that if the distances are not equal, E1 and
E2 will not be simultaneous in the common rest
frame supposed here.
LA
LS
E1
LB
E2
E0
Quantum correlations with no causal order
O Oreshkov, F Costa1, Cˇaslav Brukner
The idea that events obey a definite causal order is deeply rooted in our
understanding of the world and at the basis of the very notion of time. But
where does causal order come from, and is it a necessary property
of nature? We address these questions from the standpoint of quantum
mechanics in a new framework for multipartite correlations which does
not assume a pre-defined global causal structure. All known situations that
respect causal order, including space-like and time-like separated
experiments, are captured by this framework in a unified way.
Surprisingly, we find correlations that cannot be understood in terms of
definite causal order.
These correlations violate a “causal inequality” that is satisfied by all
space-like and time-like correlations. We further show that in a classical
limit causal order always arises, suggesting that space-time may emerge
from a more fundamental structure in a quantum-to-classical transition.
4: Conclusion
Time does indeed pass! [Maudlin]. This happens at both the
micro (quantum) level and classical (macro) level.
At the micro level this need not happen simultaneously, as
determined by the macro space-time. Parts of quantum
uncertainty may lag, and only crystallize out after the
majority of events have become determinate.
The classical time-reversible Hamiltonian dynamics are not
the norm. Rather they are sometimes a good approximation to
what actually happens in the real universe, in restricted
physical circumstances. But they do not fully represent the
fundamental nature of what is going on at macro scales –or
even micro.
Common sense is right: time is not an illusion, despite what many
physicists may say. GR proper time determined along preferred
timelike world lines is the key.
Relation to proper time:
Quantum interferometric visibility as a witness of general relativistic
proper time M Zych, F Costa, I Pikovski, and C Brukner
We propose a novel quantum effect that cannot be explained without the
general relativistic notion of proper time. We consider interference of a
"clock" - a particle with evolving internal degrees of freedom - that will
not only display a phase shift, but also reduce the visibility of the
interference pattern. According to general relativity proper time flows
at different rates in different regions of space-time. Therefore, due to
quantum complementarity the visibility will drop to the extent to which
the path information becomes available from reading out the proper
time from the "clock".
Such a gravitationally induced decoherence would provide the first test
of the genuine general relativistic notion of proper time in quantum
mechanics.
To be done:
1.Find out under what condition transition surfaces can
become null and then timelike
-intense gravitational fields, like Black Hole formation?
2. Work out ADM equations when this happens
(3-metric is no longer spacelike)
Relation to quantum gravity:
Any quantum gravity theory must produce an EBU at the
macro level.
This is a criterion of a good theory
- e.g. spin foam
There is indeed a passage of time:
The past is fixed and cannot be changed.
The Moving Finger writes; and, having writ,
Moves on: nor all your Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all your Tears wash out a Word of it
-- Omar Khayyam (Poem #545)
The future is not determined till it happens.
That is guaranteed to us by quantum mechanics.
It is what is experienced in the macro world.
E: Categorization problem
A philosophical argument is that the past, present, and future
are exclusive categories, so a single event can’t have the
character of belonging to all three.
The counter is as follows: Suppose E happens at tE.
At time t1 < tE, E is in future,
At time t1 = tE, E is in present,
At time t1 > tE, E is in past.
Its category changes - that is the essence of the flow of time so this is a semantic problem, not a logical one. One needs
adequate semantic usage and philosophical categories to allow
description of this change:
Language usage can’t prevent the flow of time.
“Time does not flow: this is incoherent.”
-correct
-time does not flow, it passes.
-It is the passage of time that allows rivers to flow [Maudlin]
“It can’t pass at the rate of one second per second because
that’s not a rate it’s a dimensionless number”.
-False.
-just like rates of exchange of money, this is an operator with
two slots, each with its own units.
-They don’t cancel [Maudlin]
F: Not necessary to describe events
Davies and Rovelli claim time does not flow because it’s not
needed to describe the relations between relevant variables,
which are all that matter physically. Thus you can always get
correlations between position p(t) and momentum q(t) for a
system by eliminating the time variable: solve for t = t(q) and
then substitute to get p(t) = p(t(q)) = p(q), and time has
vanished!
Thus time may exist but it does not flow; only correlations
matter.
Response:
The latter model leaves out part of what is happening: that
does not mean it does not happen, it just means it’s a partial
model of reality, including some aspects and omitting others.
It’s a projection from spacetime to phase portrait.
Fundamentally applicability of unitary QM:
• The way physics works is that universal laws apply at the
lowest level of the hierarchy of complexity;
• The effective laws at each higher level need to be deduced
from these lower level laws by suitable coarse graining
procedures.
• In general the next higher level laws will be different from
the lower level laws.
• Thus quantum physics applies everywhere at all times on
the lower levels. It will only hold at higher levels if proved to
be so.
• Hence there is no a priori reason to believe the WdEW
equation will hold globally: it has to be shown to be so.
• And there are good reasons to believe it will not be so
(because collapse of the wave function takes place locally).